Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 1st 2014

    added to periodic ring spectrum and to periodic cohomology theory a brief paragraph on looping/delooping periodicity on the \infty-modules, with a pointer to this MO discussion

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 2nd 2014

    What’s an interesting example of a 6-periodic ring spectrum?

    And more generally for (4k+2)(4k+2)-periodicity, with kk \in \mathbb{N}. Does anything spring to mind that would follow such a pattern in periodicity?

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 2nd 2014

    This reminds me of Qiaochu’s question here.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 2nd 2014
    • (edited Nov 2nd 2014)

    Thanks, Todd. Yes, I had seen that question when looking around yesterday.

    Somehow what I am asking here should be more elementary. For instance where Qiaochu invokes the ABS orientation to explain 8-fold periodicity in manifolds from that of the KOKO-ring spectrum, here I’d be happy to just observe that KOKO is 8-periodic. But I am really wondering about 6-periodicity.

    I may be wrong, but recenty it occurred to me that the 2-periodicity in elliptic cohomology is to be thought of as related to the 2+-dimensionality of Chern-Simons theory. Because, as in this MO question there is naturally an elliptic line bundle in codimension 1 and in codimension 3, one being the point restriction of the other, and for the one in codimension 3 to have a chance to reproduce the one in codimenesion 1 by transgression, we need 2-periodicity of its fibers. If that’s the right perspective, then for 7d CS theory we’d expect to need 6-periodicity, and so that’s why I was wondering if there are any candidates for that.

    In any case, of course one may alsways force anything to become nn-periodic for any nn. But I’d be happy to see ring spectra arising “in nature” that are 6-periodic.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)